[Fis] High or low symmetry

Dear Dr. Shu-Kun Lin,

I am still not convinced. Take the dewpoint example. At high temperatures
water vapour is symmetrically (i.e. homogeneously and isotropically) mixed
into the air. At other temperatures the stable state, i.e. the state the
system equilibrates into, is a state of lower symmetry with droplet
nucleation, growth and droplet size distribution equilibration. Hence, we
cannot UNIVERSALLY say that more symmetry means more stability. At high
temperatures you are probably right, but not at ALL temperatures.

Another example is a magnetic lattice with each lattice site having spin
either up or down (so called Ising model). Again, above the Curie point the
isotropic and homogeneous state is more stable, and the fluctuations
occurring in this state decay. Below Curie point, however, the more stable
state is the one with lower symmetry (a preferred direction occurs). Again,
the fluctuations from this state decay. This is kind of commonplace in the
theory of phase transitions and critical phenomena, good reading about it
is still Stanley's book "Phase transitions and critical phenomena".

And crystal is, in fact, LESS symmetric than non-crystalline state, both
microscopically and macroscopically. It has selected directions (axes of
elementary cell), hence it is not isotropic. The disordered state (liquid)
is typically isotropic, except for the cases like liquid crystals.

This is easy to understand in terms of the co-called phase space, or the
space in which the system's microscopic states occupy a certain area. Very
simplistically, the smaller is the area, the less symmetric is the system,
as the more limitations to the possible states occur. The phase space for a
crystal is smaller than for a disordered system.

As to your homogeneous gas example, we are mixing two things here. If we
talk equilibrium states, then in equilibrium (and in the absense of
external fields) gas is typically homogeneous and isotropic. If external
fields apply (i.e. gravity), we have stable inhomogeneous state in the form
of barometric formula. And this state is more stable (in the gravity field)
than the homogeneous, equidense one.

Regards, Igor
Dr. Igor Rojdestvenski,
Dept. Plant Physiology,
Umea university,
Umea 90187,
Sweden
e-mail:
<mailto:igor.rojdestvenski@plantphys.umu.se>igor.rojdestvenski@plantphys.umu<mailto:igor.rojdestvenski@plantphys.umu.se>.se
phone: +46-73-6205020
fax: +46-90-7866676
homepage: <http://www.patronov.net>www.patronov<http://www.patronov.net>.net
Received on Tue Jul 22 12:33:44 2003